How to Calculate Acceleration

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Acceleration is the rate of change in the velocity of an object as it moves.[1] If an object maintains a constant velocity, it is not accelerating. Acceleration only occurs when the velocity of the object changes. If the object is changing velocity at a constant rate, the object is moving with constant acceleration.[2]. You can calculate the rate of acceleration, measured in meters per second, based on the time it takes you to go from one velocity to another, or based on the mass of an object.

Steps

Method One of Three:Calculating Average Acceleration from Two Velocities

Define the equation for average acceleration. You can calculate the average acceleration of an object over a period of time based on its velocity (its speed traveling in a specific direction), before and after that time. To do this you need to know equation for acceleration: a = Δv / Δt where a is acceleration, Δv is the change in velocity, and Δt is the amount of time it took for that change to occur.[3]

The unit for acceleration is meters per second per second or m/s2.

Acceleration is a vector quantity, meaning it has both a magnitude and a direction.[4] The magnitude is the total amount of acceleration whereas the direction is the way in which the object is moving. If it is slowing down the acceleration will be negative.

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Understand the variables. You can further define Δv and Δt: Δv = vf - vi and Δt = tf - ti where vf is the final velocity, vi is the initial velocity, tf is the ending time, and ti is the starting time.[5]

Because acceleration has a direction, it is important to always subtract the initial velocity from the final velocity. If you reverse them, the direction of your acceleration will be incorrect.

Unless otherwise stated in the problem, the starting time is usually 0 seconds.

Use the formula to find acceleration. First write down your equation and all of the given variables. The equation is a = Δv / Δt = (vf - vi)/(tf - ti). Subtract the initial velocity from the final velocity, then divide the result by the time interval. The final result is your average acceleration over that time.

If the final velocity is less than the initial velocity, acceleration will turn out to be a negative quantity or the rate at which an object slows down.

Example 1: A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. What is its average acceleration?

Define Newton’s Second Law of Motion. Newton’s second law of motion states that when the forces acting on an object are unbalanced, the object will accelerate. This acceleration is dependent upon the net forces that act upon the object and the object’s mass.[6] Using this law, acceleration can be calculated when a known force is acting on an object of known mass.

Newton’s law can be represented by the equation Fnet = m x a, where Fnet is the total force acting on the object, m is the object’s mass, and a is the acceleration of the object.

When using this equation, keep your units in the metric system. Use kilograms (kg) for mass, newtons (N) for force, and meters per second squared (m/s2) for acceleration.

Find the mass of your object. To find the mass of an object, simply place it on a balance or scale and find its mass in grams. If you have a very large object, you may need to find a reference that can provide you with the mass. Larger objects will likely have a mass with the unit of kilograms (kg).

For this equation, you will want to convert the mass into kilograms. If the mass you have is in grams simply divide that mass by 1000 to convert to kilograms.

Calculate the net force acting on your object. A net force is an unbalanced force. If you have two forces opposing each other and one is larger than the other, you will have a net force in the direction of the larger force.[7] Acceleration happens when an unbalanced force acts on an object, causing it to change speeds towards the direction the force is pushing or pulling it.

For example: Let’s say you and your big brother are playing tug-of-war. You pull the rope to the left with a force of 5 newtons while your brother pulls the rope in the opposite direction with a force of 7 newtons. The net force on the rope is 2 newtons to the right, in the direction of your brother.

In order to properly understand the units, know that 1 newton (N) is equal to 1 kilogram X meter/second squared (kg X m/s2).[8]

Rearrange the equation F = ma to solve for acceleration. You can change this formula around to solve for acceleration by dividing both sides by the mass, so: a = F/m. To find the acceleration, simply divide the force by the mass of the object being accelerated.

Force is directly proportional to the acceleration, meaning that a greater force will lead to a greater acceleration.

Mass is inversely proportional to acceleration, meaning that with a greater mass, the acceleration will decrease.

Use the formula to solve for acceleration. Acceleration is equal to the net force acting on an object divided by the mass of the object. Once you’ve established the values for your variables, do the simple division to find the acceleration of the object.

For example: A 10 Newton force acts uniformly on a mass of 2 kilograms. What is the object’s acceleration?

a = F/m = 10/2 = 5 m/s2

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Method Three of Three:Confirming Your Understanding

1

Understand the Direction of Acceleration. The physics concept of acceleration doesn't always match how we would use the term in everyday life. Every acceleration has a direction, usually represented as positive if it's UP or RIGHT, and negative if DOWN or LEFT. See if your answer makes sense based on this breakdown:

Understand Net Force. If more than one force acts on an object, combine them into a net force before you calculate acceleration. For a problem in two dimensions, this looks something like this:

Example Problem: April is pulling a 400 kg container right with a force of 150 newtons. Bob stand on the left of the container and pushes with a force of 200 newtons. A wind blowing left exerts a force of 10 newtons. What is the acceleration of the container?

The equation or formula for velocity is similar to the one for speed. To figure out velocity, you divide the distance by the time it takes to travel that distance, and then you add your direction to it.

A body starts from rest and acquires a velocity of 10 m/s in 2s; what's the acceleration?

Mark Cabotage

Community Answer

The formula is final velocity - initial velocity / time. The final velocity is 10 m/s, because the body's final movement as we know is 10m/s. The initial velocity is 0 m/s, because it states, "A body starts from rest." 10 m/s - 0m/s / 2 s, eventually you'll get 5 m/s/s.

How do I calculate the normal force when I have a mass of 10 kg, angle of inclination _=15, length of 10 m and the coefficient of kinetic friction = 0,15?

Community Answer

Calculating the normal force here, you will only need the mass and angle of inclination of this surface. When placing the X-axis on the ramp of your free body diagram and if the only force acting on your object of 10kg is gravity of Earth, then looking at the Y-axis of your diagram, you should see that that normal force is equal to the Y-component of the gravitational force. Considering the angle given, you should see the normal force is equal to (mass * gravityAcceleration * sin(15)).

Acceleration is defined as the change in velocity over time. For example, consider a car accelerating from a stoplight to 60 mph. Its initial velocity is zero, but over a time of several seconds, its velocity increases until it reaches 60 mph. If the car remains at 60 mph without changing velocity, then its acceleration would be zero, or zero change in velocity over time.

Net force is the sum of all the forces acting on an object. For example, the net force of two people pushing a box the same direction would be the sum of the force exerted by each person. The same goes for two people pushing against each other, but one force will be negative.

About This Article

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wikiHow Staff Editor

This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Together, they cited information from 8 references. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article meets our high standards.

To calculate acceleration, use the equation a = Δv / Δt, where Δv is the change in velocity, and Δt is how long it took for that change to occur. To calculate Δv, use the equation Δv = vf - vi, where vf is final velocity and vi is initial velocity. To caltulate Δt, use the equation Δt = tf - ti, where tf is the ending time and ti is the starting time. Once you've calculated Δv and Δt, plug them into the equation a = Δv / Δt to get the acceleration.

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